Simulation-based Inference through Random Features

科学家们利用模拟来模拟各种复杂的系统，从天文学和生态学，到气候学和金融学，再到流行病学和化学工程。一旦科学家确定了模拟模型中的所有参数，就很容易向前运行，看看它预测了什么。反过来，从结果回到参数，通常要困难得多，但这是将模型与现实世界的实际数据拟合的关键一步，因此知道哪些模拟是值得信赖的。优秀的模拟建模师会投入大量时间和精力，找出模型中数据的关键方面或“特征”，然后调整模型，使模拟输出与真实数据的特征相匹配。本项目旨在使这种基于仿真的推理接近自动化。结合机器学习和非线性动力学的思想表明，仿真模型可以通过匹配每个参数的两个随机选择的特征来拟合。该项目将通过调整基本方法来处理不同类型的数据（时间序列，空间，网络等），编写自动选择特征和调整模型参数的软件，以及开发统计方法来量化结果的不确定性，使其成为实用的通用模拟工具。这可以使使用模拟的每个科学和技术领域受益。该项目将通过一名博士后和一名研究生的参与，为STEM研究人员的培训做出贡献。科学家们越来越多地用生成模型来表达他们的想法，生成模型可以对他们研究的过程进行细粒度的模拟。用于参数推断的传统统计方法不适用于此类模型：仅评估似然函数通常在计算上难以处理，更不用说优化它了。许多基于模拟的推理技术已经发展起来，但这些技术通常需要选择多个汇总统计或特征，并调整生成模型的参数，以便在模拟中计算的汇总与在经验数据中计算的汇总相匹配。从业者通常花费相当多的精力来仔细设计这些摘要，目的是尽量减少完整数据中的信息损失。该项目将通过使用数据的随机函数，将基于模拟的推理从设计信息摘要的需要中解放出来。这借鉴了两个以前没有与基于模拟的推理相关的文献。一个是过去十年在机器学习方面的工作，它突出了“随机特征”的力量，表明基于高维数据的随机函数的预测几乎与基于数据的最优函数的预测一样好。另一个是20世纪80年代和90年代在非线性动力学方面的经典工作，它表明2d+1随机特征应该足以捕获d个潜在参数。将这些思想与基于仿真的推理的成熟结果结合起来，将提供一种简单实用的参数估计、不确定性量化和假设检验方法，适用于广泛的现代仿真模型。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Scientists use simulations to model all kinds of complex systems, from astronomy and ecology, through climatology and finance, to epidemiology and chemical engineering. Once scientists pin down all the parameters in a simulation model, it's easy to run it forward and see what it predicts. Going the other way, from outcomes back to parameters, is usually much harder, but it's the crucial step in fitting models to actual data from the real world, and so knowing which simulations are trustworthy. Good simulation modelers put lots of time and effort into working out what the crucial aspects or "features" of the data are for their models, and then adjusting their models so the simulation output matches those features of real data. This project aims to make such simulation-based inference nearly automatic. Bringing together ideas machine learning and nonlinear dynamics shows that simulation models can be fit by matching about two randomly-chosen features for every parameter. The project will make this into a practical and generic tool for simulation, by adapting the basic method to work with different types of data (time series, spatial, networks, etc.), writing software to automatically pick the features and adjust the model parameters, and developing statistical methods to quantify the uncertainty of the results. This can benefit every area of science and technology that uses simulations. The project will contribute to the training of STEM researchers through the involvement of a post-doctoral fellow and a graduate student.Scientists increasingly express their ideas in generative models which produce fine-grained simulations of the processes they study. Traditional statistical approaches to parameter inference are ill-adapted to such models: just evaluating the likelihood function is usually computationally intractable, never mind optimizing it. Many techniques of simulation-based inference have developed in response, but these typically require picking multiple summary statistics or features, and tuning the generative model's parameters so that summaries calculated on simulations match those calculated on empirical data. Practitioners often spend considerable effort on carefully designing these summaries, aiming to minimize the loss of information from the full data. This project will free simulation-based inference from the need to design informative summaries, by instead using random functions of the data. This draws on two literatures not previously connected to simulation-based inference. One is work in machine learning over the last decade, which has highlighted the power of "random features", showing that predictions based on random functions of high-dimensional data are nearly as good as predictions based on optimal functions of the data. The other is now-classic work in nonlinear dynamics from the 1980s and 1990s, which suggests that 2d+1 random features should suffice to capture d underlying parameters. Bringing these ideas together with the well-established results on simulation-based inference will provide a simple, practical methodology of parameter estimation, uncertainty quantification and hypothesis testing, applicable to a wide range of modern simulation models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.